Fraction Word Problems Worksheets - Free Printable

Problem: Identifying Fractions | Word Problems

The task involves solving word problems related to fractions. Let's go through each problem step by step.

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#### Problem 1:
Question:
A farmer has a field of 20 acres. He decides to plant corn on $\frac{3}{5}$ of the field and wheat on the remaining part. How many acres are planted with corn?

Solution:
1. The total area of the field is 20 acres.
2. The fraction of the field planted with corn is $\frac{3}{5}$.
3. To find the number of acres planted with corn, multiply the total area by the fraction:
\[
\text{Acres planted with corn} = 20 \times \frac{3}{5}
\]
4. Simplify the multiplication:
\[
20 \times \frac{3}{5} = \frac{20 \times 3}{5} = \frac{60}{5} = 12
\]

Answer:
\[
\boxed{12}
\]

---

#### Problem 2:
Question:
In a school, there are 120 students in total. If $\frac{2}{3}$ of the students are girls, how many boys are there in the school?

Solution:
1. The total number of students is 120.
2. The fraction of students who are girls is $\frac{2}{3}$.
3. To find the number of girls, multiply the total number of students by the fraction:
\[
\text{Number of girls} = 120 \times \frac{2}{3}
\]
4. Simplify the multiplication:
\[
120 \times \frac{2}{3} = \frac{120 \times 2}{3} = \frac{240}{3} = 80
\]
5. The number of boys is the total number of students minus the number of girls:
\[
\text{Number of boys} = 120 - 80 = 40
\]

Answer:
\[
\boxed{40}
\]

---

#### Problem 3:
Question:
A recipe calls for $\frac{3}{4}$ cup of sugar. If you want to make half of the recipe, how much sugar should you use?

Solution:
1. The original amount of sugar required is $\frac{3}{4}$ cup.
2. To make half of the recipe, you need half of the original amount of sugar:
\[
\text{Sugar needed} = \frac{1}{2} \times \frac{3}{4}
\]
3. Multiply the fractions:
\[
\frac{1}{2} \times \frac{3}{4} = \frac{1 \times 3}{2 \times 4} = \frac{3}{8}
\]

Answer:
\[
\boxed{\frac{3}{8}}
\]

---

#### Problem 4:
Question:
A tank is filled with water up to $\frac{5}{8}$ of its capacity. If the tank's total capacity is 64 liters, how many liters of water are currently in the tank?

Solution:
1. The total capacity of the tank is 64 liters.
2. The fraction of the tank that is filled with water is $\frac{5}{8}$.
3. To find the amount of water in the tank, multiply the total capacity by the fraction:
\[
\text{Water in the tank} = 64 \times \frac{5}{8}
\]
4. Simplify the multiplication:
\[
64 \times \frac{5}{8} = \frac{64 \times 5}{8} = \frac{320}{8} = 40
\]

Answer:
\[
\boxed{40}
\]

---

#### Problem 5:
Question:
During a sale, a store offers a discount of $\frac{1}{5}$ off the original price of an item. If the original price of the item is $75, what is the discounted price?

Solution:
1. The original price of the item is $75.
2. The discount is $\frac{1}{5}$ of the original price.
3. Calculate the discount amount:
\[
\text{Discount amount} = 75 \times \frac{1}{5}
\]
4. Simplify the multiplication:
\[
75 \times \frac{1}{5} = \frac{75}{5} = 15
\]
5. Subtract the discount from the original price to find the discounted price:
\[
\text{Discounted price} = 75 - 15 = 60
\]

Answer:
\[
\boxed{60}
\]

---

Final Answers:

1. \(\boxed{12}\)
2. \(\boxed{40}\)
3. \(\boxed{\frac{3}{8}}\)
4. \(\boxed{40}\)
5. \(\boxed{60}\)